In general, in a filtering operation which carries out a digital data processing such as an image processing, a conversion processing is carried out by taking data around the coordinates of data to be processed into this coordinate data. However, at the edge of an area for which data is available (“data end portion”), the data is discontinued, and data that is necessary for a filtering operation becomes insufficient. Therefore, the data after the processing is degraded. Consequently, it is necessary to complement the shortage of data, as shown in FIG. 1. In FIG. 1, a reference numeral 11 denotes data, a reference numeral 12 denotes start of the data 11, and a reference numeral of 13 denotes end of the data 11. A reference numeral 14 denotes a portion of data that is necessary for the processing. A reference numeral 15 denotes a portion of data that need to be complemented.
Conventionally, when data coordinates that are necessary for a filtering operation are outside of the portion of the image data, there has been known a method of complementing the insufficient data by using the coordinates that are obtained by returning the coordinates at the edge of the image data. Assume, for example, that image data at coordinates X={0, 1, 2, 3, 4, 5, 6, 7} are available, and that data at coordinates i={−2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are necessary for the filtering operation, so that the filtering operation requires image data that is not available. In this case, coordinates i′ ={1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 7, 6} that include returns of coordinates at the end portions of the image data are used, in place of the data coordinates i.
FIG. 2 is a conceptional diagram of a 4×4 filter to explain this return method. For example, as shown in FIG. 2, assume that an area (a shaded area) 22 enclosed by the coordinates (6, 2) to (9, 5) is needed to carry out a filtering operation of an image data 21 for coordinates (X, Y)=(6, 2). In this case, the coordinates of the image data are returned at the data endportion, and the X coordinate “8” is changed to “7”, and the X coordinate “9” is changed to “6”. In other words, the coordinates of (8, 2) to (9, 5) that are at the outside of the range of the image data 21 are changed to the coordinates (7, 2) to (6, 5). With such processing, it is possible to complement the shortage of data that is necessary for the filtering operation. Therefore, the discontinuity of the data end portion is reduced, and there is small influence to the data after the conversion. Consequently, degradation of the data is not so noticeable.
Further, in order to reduce data degradation due a shortage of data that is necessary for a filtering operation at the end of the image data, there is a method of increasing the resolution of the data at the end of the image data. As a data range necessary for a filtering operation is determined in a pixel unit, a range in which the degradation occurs at the data end portion is also determined in a pixel unit of an image. Therefore, when the resolution of data end portion proximity area 27 of an image data 26 is increased as shown in FIG. 3, it becomes possible to narrow an apparent data degradation range (an area shown by shaded lines) 28.
However, according to the above two conventional methods, as shown in FIG. 4, data 31 of eight pixels before a processing is complemented with data 32 of eight pixels, for example. A processing is carried out using data 33 of sixteen pixels. At the time of restoration, data 34 of eight pixels is left, and data 35 of the remaining eight pixels is abandoned. Therefore, it is not possible to avoid data degradation due to a discontinuity of the data at the data end portion.